Structure of optimal strategies in earthquake prediction

Abstract

Prediction of a stationary sequence of strong events is considered. The prediction uses any information that is related in a stationary way to the sequence. The goal of prediction is stated as minimization of a loss function which is a function of two long-term errors: the fraction of failures-to-predict and the fraction of alarm time. We describe the structure of optimal prediction strategies for any convex loss function given a time-varying hazard function. Prediction stability is analyzed within the framework of this loss-function approach. The main result of this work may be regarded as a rigorous formulation and refinement of some earthquake prediction algorithms.